Time-Averaged Template for Stochastic Gravitational-Wave Background Detection in Space-Based Interferometers

TL;DR

This paper addresses SGWB parameter estimation for space-based interferometers with time-varying arm-lengths by comparing three template strategies: time-averaged, equal-arm, and an arm-length–free model. It develops a frequency-domain Bayesian framework using a Whittle likelihood and segment-wise, time-averaged TDI responses to capture orbital dynamics, and it demonstrates that time-averaged templates substantially improve parameter accuracy over the conventional equal-arm approach for long-duration data. Introducing an effective arm-length as a free parameter increases uncertainty and can bias instrumental-noise estimates, though Bayes factors indicate some gain in describing data with arm-length variability for shorter datasets. The study highlights the importance of realistic, segment-based template construction for high-precision SGWB analysis in missions like LISA and Taiji, and it points to future work on flexible spectra, per-direction arm-length treatments, and additional instrumental noises to further close the gap to real data.

Abstract

Stochastic gravitational-wave background (SGWB) poses significant challenges for data analysis and parameter inference in future space-based gravitational-wave missions, such as LISA and Taiji, as it appears as an additional stochastic component along with instrumental noise. Previous studies have developed various approaches to distinguish the SGWB from instrumental noise, often under simplified assumptions such as static or equal-arm configurations. However, in realistic scenarios, time-varying arm-lengths introduce additional complexities that require careful modeling. In this work, we investigate the impact of template construction on SGWB parameter estimation under realistic orbital configurations. Using the simulated SGWB signals and dominant instrumental noise sources, we compare three template strategies: time-averaged template constructed from segmented data, equal-arm template, and a template treating the arm-lengths as a free parameter. Our results show that the time-averaged template yield improves parameter estimation accuracy under time-varying arm-lengths, whereas introducing the effective arm-length as a free parameter increases estimation uncertainty. These findings highlight the importance of realistic template construction for high-precision SGWB analysis in future space-based missions.

Figures (9)

• Figure 1: The schematic diagram of the links for Taiji, which orbits around the Sun. The triangular constellation consists of three spacecraft labeled $\vb{x}_1$, $\vb{x}_2$, $\vb{x}_3$. Each spacecraft is equipped with two optical benches designed to monitor distance changes, thereby defining six single-link interferometric arms. The subscript of the light travel time $L_{\text{rs}}$ denotes the specific direction of the link, running from the sender $\vb{x}_\text{s}$ to the receiver $\vb{x}_\text{r}$.
• Figure 2: Simulated time series of $X$ channel. The data includes the SGWB (Eq. \ref{['eq:gwx']}) and the combined instrumental noise (Eq. \ref{['eq:noisex']}). The time series spans a duration of one year and is sampled at a frequency $f_s=0.1~\text{Hz}$. With the adopted SGWB parameters, $\Omega_0=3\times10^{-12}$ and $\gamma=-1$, the SNR at $X$ for the total observation period is approximately 79.
• Figure 3: Comparison of the PSD of the simulated data and the theoretical model at $X$. The figure explicitly shows the contribution of the SGWB (Eq. \ref{['eq:gwx']}) and the combined instrumental noise (Eq. \ref{['eq:noisex']}) in comparison with the total observed PSD.
• Figure 4: Marginalized posterior distributions for the model parameters $\vb{\theta}$ obtained using time-averaged frequency-domain template. The black solid line shows the injected parameter values. The vertical lines in the diagonal panels show the median and the $68\%$ CI. The contour lines in the off-diagonal panels represent the standard $1\sigma$, $2\sigma$, and $3\sigma$ iso-probability-density levels.
• Figure 5: The reconstructed PSD for the SGWB and the instrumental noise at $X$. The solid blue curve denotes the theoretical PSD of the SGWB, the dashed red curve represents the acceleration noise, and the dash-dotted green curve corresponds to the optical metrology system noise. The lightly shaded regions in the respective colors indicate the 95$\%$ CI.